I also use jazz sneakers at times, as they provide a fair amount of arch support. I'll use ghillies when I need a good point, or when I'm at an event where looks matter (ball or demo). Personally, I think people should wear whatever dance shoe suits their needs, especially if there are any health/comfort issues. BUT some types of shoes do promote better footwork among those of us who are basically healthy in the legs. Ballet slippers, ghillies and jazz shoes (the kind with the tiny bit of heel) seem to work equally well in the kid's classes I teach - I probably wouldn't allow a heavier shoe (even a dance sneaker) unless medically necessary.
Isn't dancing in bare feet kind of unhygienic? Again, "my" kids like it but I insist on shoes for any dancing at socials and balls.